code: def lpmax(f, constr):
      """return maximum of linear equation ``f`` under
      linear constraints expressed using Ge, Le or Eq.
  
      All variables are unbounded unless constrained.
  
      Examples
      ========
  
      >>> from sympy.solvers.simplex import lpmax
      >>> from sympy import Eq
      >>> from sympy.abc import x, y
      >>> lpmax(x, [2*x - 3*y >= -1, Eq(x+ 3*y,2), x <= 2*y])
      (4/5, {x: 4/5, y: 2/5})
  
      Negative values for variables are permitted unless explicitly
      exluding:
  
      >>> lpmax(x, [x <= -1])
      (-1, {x: -1})
  
      If a non-negative constraint is added for x, there is no
      possible solution:
  
      >>> lpmax(x, [x <= -1, x >= 0])
      Traceback (most recent call last):
      ...
      sympy.solvers.simplex.InfeasibleLPError: inconsistent/False constraint
  
      See Also
      ========
      linprog, lpmin
      """
      return _lp(max, f, constr)
  
imports: from sympy.core import sympify
  from sympy.core.exprtools import factor_terms
  from sympy.core.relational import Le, Ge, Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy
  from sympy.core.sorting import ordered
  from sympy.functions.elementary.complexes import sign
  from sympy.matrices.dense import Matrix, zeros
  from sympy.solvers.solveset import linear_eq_to_matrix
  from sympy.utilities.iterables import numbered_symbols
  from sympy.utilities.misc import filldedent
label_desc: Use image node_id 11 for calling a global function with example usage: lpmax(f, constr) and returns: _lp